Find : sqrt{7+2 sqrt{10}} | vedclass

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Question

(D) Let $\sqrt{7+2 \sqrt{10}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $7 + 2 \sqrt{10} = x + y + 2 \sqrt{xy}$.Comparing the rational and irr

Vedclass · Accepted Answer

$\sqrt{5}+\sqrt{2}$

Vedclass · Answer

(D) Let $\sqrt{7+2 \sqrt{10}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $7 + 2 \sqrt{10} = x + y + 2 \sqrt{xy}$.Comparing the rational and irrational parts,we have $x + y = 7$ and $2 \sqrt{xy} = 2 \sqrt{10}$,which implies $xy = 10$.We need two numbers whose sum is $7$ and product is $10$.The factors of $10$ are $(5, 2)$ such that $5 + 2 = 7$ and $5 	imes 2 = 10$.Thus,$x = 5$ and $y = 2$.Therefore,$\sqrt{7+2 \sqrt{10}} = \sqrt{5} + \sqrt{2}$.

Find : $\sqrt{7+2 \sqrt{10}}$

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